I don't recall the Dead covering many Beatles songs.
Garcia did an intense Dear Prudence, and "I Saw Her Standing There" on his solo album; they covered the reprise of Jude in a segue from Dear Mr. Fantasy (Traffic). Later on they covered Lucy. Can't think of too many others. They probably covered more Dylan tunes than anyone else,though.
Wasn't me made the statement, was someone else....I've never been much of a rock fan so I have no real clue about what the Dead did